Solve for $x$ : $x^2 + 16x + 63 = 0$
Solution: The coefficient on the $x$ term is $16$ and the constant term is $63$ , so we need to find two numbers that add up to $16$ and multiply to $63$ The two numbers $7$ and $9$ satisfy both conditions: $ {7} + {9} = {16} $ $ {7} \times {9} = {63} $ $(x + {7}) (x + {9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 7) (x + 9) = 0$ $x + 7 = 0$ or $x + 9 = 0$ Thus, $x = -7$ and $x = -9$ are the solutions.